Hiroshima University Syllabus

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Japanese
Academic Year 2024Year School/Graduate School School of Science
Lecture Code HB282000 Subject Classification Specialized Education
Subject Name 数理解析学B
Subject Name
(Katakana)
スウリカイセキガクB
Subject Name in
English
Mathematical Analysis B
Instructor KAMIMOTO SHINGO
Instructor
(Katakana)
カミモト シンゴ
Campus Higashi-Hiroshima Semester/Term 4th-Year,  First Semester,  2Term
Days, Periods, and Classrooms (2T) Mon7-8,Weds3-4:SCI E211
Lesson Style Lecture Lesson Style
(More Details)
 
Lectures are given face-to-face or online depending on the situation. 
Credits 2.0 Class Hours/Week   Language of Instruction B : Japanese/English
Course Level 4 : Undergraduate Advanced
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students
Keywords Holomorphic functions of several variables, Analytic differential equation, Regular singular point, The Cauchy-Kowalewski theorem, Zerner's theorem. 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
 
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students)
Mathematics
(Knowledge and Understanding)
・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics. 
Class Objectives
/Class Outline
We learn the basics of the theory of analytic differential equations. 
Class Schedule lesson1 Power series and the domain of convergence
lesson2 Radius of convergence
lesson3 Holomorphic functions of several variables
lesson4 Cauchy's integral representation
lesson5 Existence and uniqueness of solutions of analytic ordinary differential equations
lesson6 Analytic continuation of solutions of ordinary differential equations
lesson7 Analytic solutions of linear ordinary differential equations
lesson8 Monodromy representations
lesson9 Regular singular points
lesson10 The Frobenius method
lesson11 Initial value problem for partial differential equations
lesson12  The Cauchy-Kowalewski theorem
lesson13 Zerner's theorem
lesson14  Bicharacteristic strip
lesson15 Propagation of singularity 
Text/Reference
Books,etc.
If you can read Japanese books, please check the syllabus of this course written in Japanese. Otherwise, please consult at the classroom. 
PC or AV used in
Class,etc.
 
(More Details) Black board 
Learning techniques to be incorporated  
Suggestions on
Preparation and
Review
Lesson1 - Lesson4 Understand fundamental properties of holomorphic functions of several variables.
Lesson5 - Lesson8 Study properties of analytic solutions of analytic ordinary differential equations.
Lesson9 - Lesson10 Study behaviors of solutions at singular points.
Lesson11 - Lesson15 Study analyticity of solutions of analytic partial differential equations. 
Requirements  
Grading Method Reports (90%), Class participation (10%). 
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
Message  
Other   
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. 
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